The long range objectives of this research are to further the understanding of the dynamical behavior of aggregates of interacting cells, and to apply this knowledge to problems of cell movement and pattern formation in developmental biology and to problems in physiology. The research falls into four major categories: (1) studies on pattern formation in development, (2) studies on chemotaxis, (3) studies on excitable systems, and (4) studies on cardiac dynamics. The aim under (1) is to develop and analyze models for mound formation in the cellular slime mold Dictyostelium discideum that incorporate pacemakers, cAMP production and diffusion, cell-cell interactions, cell differentiation and cell sorting. The aim in (2) is to develop and analyze a model for bacterial adaptation and to do simulations of aggregation in three-dimensional concentration fields. The major objective in (3) is to study models of calcium channel dynamics in oocytes with a view toward understanding the effect of different types of calcium channels on the stimulus-response characteristics and the propagation of waves. The aims under (4) are (I) to develop an integrated model for calcium dynamics and the membrane potential in cardiac myocytes in order to understand spontaneous calcium release, and (ii) to study the role of anisotropy in the genesis of fibrillation in ventricular tissue. The results of parts (l) and (2) of this research will advance our understanding of several basic processes in developmental biology: signal transduction, cell-cell signaling, cell and tissue motion and spatial pattern formation. A better understanding of these processes will contribute to a better understanding of how systems respond to their environment, how normal development can be disrupted, and how certain components of the immune system function. The results of the work described under (3) and (4) will further our understanding of one of the major public health problems in the US, sudden cardiac death, which claims approximately 1000 individuals per day. Most result from a rapid irregular rhythm called ventricular fibrillation, which often evolves from ventricular tachycardia. The results of the proposed work will contribute to our understanding of two important aspects of the genesis of arrhythmias. Firstly, single-cell models that incorporate current knowledge about membrane dynamics and calcium handling will advance our understanding of how these components interact and how this interaction can produce ventricular tachycardia locally. Secondly, integrating the single-cell dynamics into a large-scale model of cardiac tissue will provide insight into how aberrant local behavior can be suppressed by interaction with neighboring tissue, what the critical space scale of abnormality is for production of large-scale (tissue-wide) disruption of propagation, and how supercritical local abnormalities evolve in time. A better understanding of the different mechanisms that can give rise to ventricular tachycardia and an understanding of how it evolves into ventricular fibrillation may lead to new strategies for suppressing them and thereby have an important impact on public health.